Topic 2 of 7 · Form 5
Solid geometry: projections, true lengths and true shapes
First and third angle projection; principal views; hidden detail; projection symbols.
Notes for this topic 1 file, in order
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Orthographic projection
First and third angle projection; principal views; hidden detail; projection symbols.
Auxiliary projection
- First auxiliary view: projected onto a plane perpendicular to one principal plane – used to find the true shape of an inclined surface.
- Second auxiliary view: used for oblique surfaces (inclined to all principal planes).
True length of a line
A line appears at true length in a view parallel to it. Methods: rotation (revolving the line into a principal plane) and auxiliary projection.
True angle and true shape
- True inclination of a line to the horizontal plane appears in the elevation when the line is parallel to the vertical plane.
- True shape of a section: project the cutting plane onto an auxiliary plane parallel to it.
Points, lines and planes
Traces of planes, the intersection of two planes, the angle between a line and a plane, and the dihedral angle between planes.
Exam tip: Label every point consistently in all views (a, a′, a₁) – it prevents projection errors.
Check yourself
- When does a line appear at its true length?
- What is the purpose of an auxiliary view?
- How is the true shape of a sloping section found?
Show answers
- In a view on a plane parallel to the line.
- To show the true shape of an inclined surface not parallel to a principal plane.
- By projecting the cut onto an auxiliary plane parallel to the cutting plane.
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